Simplify the following expression: $p = \dfrac{-5n^2 + 40n - 60}{n - 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ p =\dfrac{-5(n^2 - 8n + 12)}{n - 6} $ Then we factor the remaining polynomial: $n^2 {-8}n + {12} $ ${-6} {-2} = {-8}$ ${-6} \times {-2} = {12}$ $ (n {-6}) (n {-2}) $ This gives us a factored expression: $\dfrac{-5(n {-6}) (n {-2})}{n - 6}$ We can divide the numerator and denominator by $(n + 6)$ on condition that $n \neq 6$ Therefore $p = -5(n - 2); n \neq 6$